A shift-splitting Jacobi-gradient iterative algorithm for solving the matrix equation A𝒱−𝒱‾B=C

To improve the convergence of the gradient iterative (GI) algorithm and the Jacobi-gradient iterative (JGI) algorithm [Bayoumi, Appl Math Inf Sci, 2021], a shift-splitting Jacobi-gradient iterative (SSJGI) algorithm for solving the matrix equation is presented in this paper, which is based on the splitting of the coefficient matrices. The proposed algorithm converges to the exact solution for any initial value with some conditions. To demonstrate the effectiveness of the SSJGI algorithm and to compare it to the GI algorithm and the JGI algorithm [Bayoumi, Appl Math Inf Sci, 2021], numerical examples are provided.